i^i ```Name: Dunny P. Status: student Age: N/A Location: N/A Country: N/A Date: N/A ``` Question: I am having a hard time trying to figure out how to raise the imaginary unit i to the imaginary power i. In other words: i^i = ? Where can I find more information on complex forms of Ln? Replies: Raising complex numbers to powers is often simplified by using Euler's Formula: exp(i*x) = cos(x) +i*sin(x) You see for example, that for x=pi this becomes exp(i*pi) = -1 since sin(pi)=0. Similarly, exp(i * pi/2) = i, since cos(pi/2) = 0 and sin(pi/2) = 1 So i^i = [exp(i*pi/2)]^i = exp(i^2 *pi/2) = exp(-1*pi/2) = 0.207879... WHICH IS REAL! AMAZING these complex numbers! I think you will have to consult a textbook on complex variables to get detailed info on log functions of complex numbers, and of trig functions. Vince Calder Click here to return to the Mathematics Archives

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